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# KCC's Quizzes on AQQ256 about square roots in the digital world

Quiz of the week: AQQ256 - making square root within integer numbers world.

Good luck! And try to be among the firsts!

Kuo-Chang

P.S. Don't hesitate to share those weekly quizzes in EZ to colleagues or friends!

Updated text.
[edited by: emassa at 7:52 PM (GMT -4) on 22 Mar 2024]
Parents
• My thought process…

I’m going to call K = 12345678987654321 for simplicity.

N has to be divisible by 9 since the sum of the numbers in K are divisible by 9.

Since the answer (K) ends in a 1 and it’s the square of a number, N must end in a 1 or 9 since those are the only two numbers whose square is a 1 (1 and 81).

I note that N has to lie within the bounds of 100,000,000 (which gives 17 digits as an answer), and 1,000,000,000,000 (lowest to give 18 digits), so it will be a 9 digit number.

I notice there is a similarity in K with the square of 11 (= 121) and 111 (12321) as the pattern of increasing numbers and decreasing numbers are shared.

Make a guess that the solution (N) may be made up of only the digit 1 (ie, 1111….) and since the solution must be divisible by 9, as well as be a 9 digit number, I guess the solution is…

N = 111,111,111

Plugging into N2 reveals the guess was correct!  N2 = 12345678987654321.

- Brian

• My thought process…

I’m going to call K = 12345678987654321 for simplicity.

N has to be divisible by 9 since the sum of the numbers in K are divisible by 9.

Since the answer (K) ends in a 1 and it’s the square of a number, N must end in a 1 or 9 since those are the only two numbers whose square is a 1 (1 and 81).

I note that N has to lie within the bounds of 100,000,000 (which gives 17 digits as an answer), and 1,000,000,000,000 (lowest to give 18 digits), so it will be a 9 digit number.

I notice there is a similarity in K with the square of 11 (= 121) and 111 (12321) as the pattern of increasing numbers and decreasing numbers are shared.

Make a guess that the solution (N) may be made up of only the digit 1 (ie, 1111….) and since the solution must be divisible by 9, as well as be a 9 digit number, I guess the solution is…

N = 111,111,111

Plugging into N2 reveals the guess was correct!  N2 = 12345678987654321.

- Brian

Children